Problem: The sum of two angles is $76^\circ$. Angle 2 is $108^\circ$ smaller than $3$ times angle 1. What are the measures of the two angles in degrees?
Explanation: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 76}$ ${y = 3x-108}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${3x-108}$ for $y$ in the first equation. ${x + }{(3x-108)}{= 76}$ Simplify and solve for $x$ $ x+3x - 108 = 76 $ $ 4x-108 = 76 $ $ 4x = 184 $ $ x = \dfrac{184}{4} $ ${x = 46}$ Now that you know ${x = 46}$ , plug it back into $ {y = 3x-108}$ to find $y$ ${y = 3}{(46)}{ - 108}$ $y = 138 - 108$ ${y = 30}$ You can also plug ${x = 46}$ into $ {x+y = 76}$ and get the same answer for $y$ ${(46)}{ + y = 76}$ ${y = 30}$ The measure of angle 1 is $46^\circ$ and the measure of angle 2 is $30^\circ$.